Question

Is there a relatively compact way of writing the solution to:
\[ \int_ \frac{\cos(x)^n}{\sin(x)^m} dx \] and \[ \int_ \frac{\cos(x)^n}{\sin(x)^m} dx \] ?

Answer 1

what's that sin^n(x) or sin(x^n)?

Answer 2

\[\int\limits\frac{(\cos(x))^n}{(\sin(x))^m}\]\[\int\limits\frac{(\cos(x))^m}{(\sin(x))^n}\]

Answer 3

is it indefinite or are there limits?

Answer 4

Indefinite

Answer 5

Damn!! this isn't nice ... you assume m > n or n > m and use integration by parts n or m times ...

Answer 6

also changing sine and cosine into complex form might work ... .

Answer 7

That's weird, you'd have the imaginary part of e^ix above and real part below, or vice-versa.

Answer 8

yeah ... just take Real part ... ignore imaginary part.

Answer 9

Does that mean leave sin as sin?

Answer 10

If you're doing cos/sin